Mesoscale structures of turbulent sprays

Abstract

Mesoscale structural phenomena, mechanisms, and the logarithmic law of decay of the group combustion modes of clusterlike structures in turbulent premixed sprays were examined analytically and the results compared with recent experimental results. A universal law of cluster gasification was obtained in the form of the normalized functions, which are dependent on the cluster's interior and exterior fluid flow structures, cluster parameters, and environmental conditions. The results were used to formulate the law of the decay of the probability, P I , of an internal group combustion mode of a cluster as the function of the geometrical group combustion number, G C , the gasification functions, and the non-dimensional parameters of the micro- and mesoscale aerothermochemical processes of droplets and clusters. The transition in the group combustion mode of a member cluster of iso- G C family, expressed self-consistently in the form of a logarithmic decaying law, ln P I =ln B −e ln G C , and alternatively by a power law, P I = B(G C ) −e , in the broad ranges of a cluster's group combustion number, G C , and other parameters of turbulent sprays, was found to be in agreement with the recent experimental results of turbulent sprays found by Akamatsu et al. The decay parameters, e and B , of clusters were also determined as the functions of mesoscopic structural partition functions. The decay parameters B and e of the mean cluster are estimated to be 0.152 and 0.278, respectively, from the experimental data. The group mode index, Λ, defined by the Damkohler number, gasification correction factor, and energy functions has been introduced to describe the departure of the probability of the group combustion of a member cluster from that of the mean cluster in an iso- G C family. Those clusters with Λ>1 exhibit high probability of internal group combustion, and clusters with Λ